Question: Rewrite as a simplified fraction. ${2.3\overline{4} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 234.4444...\\ 10x &= 23.4444...\end{align*}}$ Subtracting the two equations, we have: ${90x = 211}$ ${x = \dfrac{211}{90}} \text{or} {2 \dfrac{31}{90}}$